How do you find $lim x-sqrtx$ as $x->oo$ ?

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Answer 1 · 2017-02-04T23:59:15

$lim_(x->oo) (x-sqrt(x)) = +oo$

Write the function as:

$f(x) = x-sqrt(x) = sqrt(x) (sqrt(x) -1)$

As:

$lim_(x->oo) sqrt(x) = +oo$

and

$lim_(x->oo) sqrt(x)-1 = +oo$

then also:

$lim_(x->oo) sqrt(x)(sqrt(x)-1) = +oo$

How do you find lim x-sqrtxlim x-sqrtx as x->oox->oo?